Problem: Find the zeros of the function. Enter the solutions from least to greatest. $h (x)=(-4x -5)(-x +5)$ $\text{lesser }x = $
For any two expressions $A$ and $B$ : If $A\cdot B=0$ then either $A=0$ or $B=0$. This is called the zero product property. In our case, $(-4x -5)(-x +5)=0$. So either $(-4x -5)=0$ or $(-x +5)=0$ : $\begin{aligned} (1)&&-4x -5&=0 \\\\ &&-4x&=5 \\\\ &&x&=-\dfrac{5}{4} \end{aligned}$ $\begin{aligned} (2)&&-x +5&=0 \\\\ &&-x &= -5 \\\\ &&x&=5 \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= -\dfrac{5}{4} \\\\ \text{greater } x &= 5 \end{aligned}$